$25.$ a$.$ Use a spreadsheet to answer this question and assume the yield curve is flat at a level of $4\%.$Calculate the convexity of a bullet fixed$-$income portfolio, that is$,$ a portfolio with a singlecash flow. Suppose a single $$1,000$ cash flow is paid in year $5.$b$.$ Now calculate the convexity of a ladder fixed$-$income portfolio, that is$,$ a portfolio withequal cash flows over time. Suppose the security makes $$100$ cash flows in each of years$19,$ so that its duration is close to the bullet in part $($a$).$c$.$ Do ladders or bullets have greater convexity?